Recall that Bary-Soroker–Fehm–Petersen [1]} proved that the product of two varieties with the Hilbert property also satisfies the Hilbert property.
Their result gives an affirmative answer to an old question of Serre (asked in [2]}).
Note that Bary-Soroker–Fehm–Petersen's theorem can also be deduced from [3]}, which builds on [4]}.
